We present a time-lapse sequence of 20 near-infrared (J- and K'-band) snapshots of the central 20'' x 20'' of the Crab pulsar wind nebula, taken at sub-arcsecond resolution with the Hokupa'a/QUIRC adaptive optics camera on the Gemini North Telescope, and sampled at intervals of 10 minutes and 24 hours. It is observed that the equatorial wisps and polar knots in the termination shock of the pulsar wind appear to fluctuate in brightness on kilosecond time-scales. Maximum flux variations of {+-}24 {+-} 4 and {+-}14 {+-} 4 per cent relative to the mean (in 1.2 ks) are measured for the wisps and knots respectively, with greatest statistical significance in J band where the nebula background is less prominent. The J and K' flux densities imply different near-infrared spectra for the nonthermal continuum emission from the wisps and outermost polar knot (''sprite''), giving F{sub {nu}} {proportional_to} {nu}{sup -0.56{+-}0.12} and F{sub {nu}} {proportional_to} {nu}{sup -0.21{+-}0.13} respectively. The data are compared with existing optical and UV photometry and applied to constrain theories of the variability of the wisps (relativistic ion-cyclotron instability) and knots (relativistic fire hose instability)
